Multiple spatial coherence resonances induced by white gaussian noise in excitable network composed of Morris-Lecar model with class Ⅱ excitability

Li Yu-Ye; Jia Bing; Gu Hua-Guang

doi:10.7498/aps.61.070504

Abstract

To study the effect of noise on the network and the influence of noise on the spatio-temporal behaviors of the network, a homogeneous network of excitable cells is constructed, in which the classical Morris-Lecar neuron model behaves as a unit by electric coupling to neighbouring ones. The deterministic behavior of each unit is a resting state corresponding to class Ⅱ excitability. Under the action of white Gaussian noise in the network, spiral wave can be induced within a large range of noise intensity, while disordered spatiotemporal structure is induced within a certain small intensity range. With the increase of noise intensity, spiral wave is characterized by a transition back and forth between simple structure and complex structure, or appears alternately with the disordered structure. By calculating spatial structure function and signal-to-noise ratio (SNR), it is found that the SNR of spiral wave with a simple structure is higher and the SNR becomes lower when the spiral wave has a complex or an even disordered structure. The SNR curve shows that multiple peaks appear with the increase of noise intensity, which indicates that white Gaussian noise can induce the multiple spatial coherence resonance in an excitable cellular network, and suggests that there are many opportunities to select diverse intensity noises to be rationally used in a realistic excitable system.

Keywords:

Authors and contacts

1.
College of Life Sciences, Shaanxi Normal University, Xi’an 710062, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos 11072135 and 10772101), and the Fundamental Research Funds for the Central Universities (Grant No. GK200902025).

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Cited By

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2]
[3]	Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365337
[4]
[5]	Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130
[6]
[7]	Hu G, Ditzinger T, Ning C, Haken H 1993 Phys. Rev. Lett. 71 807
[8]
[9]	Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101
[10]	Carrillo O, Santos M A, Garca-Ojalvo J, Sancho J 2004 Europhys.Lett. 65 452
[11]
[12]	Perc M 2005 Phys. Rev. E 72 016207
[13]
[14]
[15]	Yi M, Jia Y, Liu Q, Zhan X 2008 Acta. Phys. Sin. 57 621 (in Chinese)[易鸣, 贾亚, 刘泉, 詹璇 2008 57 621]
[16]	Higgs M H, Slee S J, Spain W J 2006 J. Neurosci. 26 8787
[17]
[18]
[19]	Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G,Ren W 2009 Chin. Phys. Lett. 26 110501
[20]
[21]	Yuan L, Liu Z Q, Zhang H M, Ding X L, Yang M H, Gu H G, RenW 2011 Chin. Phys. B 20 020508
[22]	Perc M 2007 Chaos Soliton. Fract. 31 64
[23]
[24]	Sun X J, Lu Q S 2010 Chin. Phys. B 19 040504
[25]
[26]	Zheng Y H, Lu Q S, Wang Q Y 2009 Int. J. Mod. Phys. C 20 469
[27]
[28]	Sun X J, Perc M, Lu Q S, Kurths J 2010 Chaos 20 033116
[29]
[30]	Wang Q Y, Chen G R, Perc M 2011 PloS ONE 6 e15851
[31]
[32]
[33]	Ma J, Wang C N, Jin W Y, Wu Y 2010 Appl. Math. Comput. 2173844
[34]	Gosak M, Marhl M, Perc M 2009 Physica D 238 506
[35]
[36]	Horikawa Y 2001 Phys. Rev. E 64 031905
[37]
[38]	Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009Chin. Phys. Lett. 26 030504
[39]
[40]
[41]	Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010Physica A 389 2642
[42]	Tateno T, Pakdaman K 2004 Chaos 14 511
[43]
[44]	Tsumoto K, Kitajima H, Yoshinaga T, Aihara K, Kawakami H2006 Neurocomputing 69 293
[45]
[46]
[47]
[48]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[49]
[50]	Hodgkin A 1948 J. Physiol. 107 165
[51]
[52]	Rinzel J, Ermentrout G B 1989 Analysis of neural excitability andoscillations (Cambridge:The MIT Press) p135
[53]
[54]	Tsubo Y, Takada M, Reyes A D, Fukai T 2007 Euro. J. Neurosci.25 3429
[55]
[56]
[57]	Tateno T, Robinson H 2007 Biophys. J. 92 683
[58]	Tateno T, Harsch A, Robinson H 2004 J. Neurophysiol. 92 2283
[59]
[60]	Prescott S A, Ratt S, De Koninck Y, Sejnowski T J 2008 J. Neurophysiol.100 3030
[61]
[62]	Stiefel KM, Gutkin B S, Sejnowski T J 2009 J. Comput. Neurosci.26 289
[63]
[64]
[65]	Liu Y H, Yang J, Hu S J 2008 J. Comput. Neurosci. 24 95
[66]
[67]	Gutkin B S, Ermentrout G B, Reyes A D 2005 J. Neurophysiol. 941623
[68]	Galn R F, Ermentrout G B, Urban N N 2005 Phys. Rev. Lett. 94158101
[69]
[70]	Phoka E, Cuntz H, Roth A, H usser M 2010 PLoS Comput. Biol.6 e1000768
[71]
[72]	Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2004 Chin. Phys.13 1396
[73]
[74]	Bogaard A, Parent J, Zochowski M, Booth V 2009 J. Neurosci. 291677
[75]
[76]	Galn R F, Bard Ermentrout G, Urban N N 2007 Neurocomputing70 2102
[77]
[78]
[79]	Gu H G, Ren W, Lu Q S, Wu S G, Chen W J 2001 Phys. Lett. A285 63
[80]	Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011Int. J. Mod. Phys. B 25 3977
[81]
[82]	Jia B, Gu H G, Li Y Y 2011 Chin. Phys. Lett. 28 090507
[83]
[84]	Rowat P 2007 Neural Comput. 19 1215
[85]
[86]
[87]	Fink C G, Booth V, Zochowski M 2011 PLoS Comput. Biol. 7e1002062
[88]
[89]	Vilar J, Rubi J 1997 Phys. Rev. Lett. 78 2882
[90]
[91]	Jiang Y 2005 Phys. Rev. E 71 057103
[92]	Liu Z H, Zhou Y R, Zhang A Y, Pang X F 2010 Acta. Phys.Sin.59 699 (in Chinese)[刘志宏, 周玉荣, 张安英, 庞小峰 2010 59 699]
[93]

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Vol. 61, Issue 7 - 2012-04-05

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